I did an engraving task with the flow set up in Dorico’s default 12-EDO tonality system. I have since wanted to hear what the piece would sound like in open Pythagorean tuning. So, on a renamed copy:
In Write mode, on the Panels toolbar, clicked “Key Signatures, Tonality Systems, and Accidentals”.
Expanded the list under “Tonality System”.
Under “Equal temperament (12-EDO)” (the default presentation), clicked the second icon, “Duplicate Tonality System”.
In the “Edit Tonality System” window that opens, renamed it to Open Pythagorean and saved it, making no other changes.
“Open Pythagorean” then appeared in the list under “Tonality System.”
Changed the tonality system of the piece to “Open Pythagorean”, following the procedure in the Dorico 6.0 / 6.1 manual “Changing the tonality system”.
Checked and confirmed that all accidentals remained.
“Undid” the tonality change to restore the piece to the original “Equal temperament (12-EDO)”.
Checked and confirmed that all accidentals remained.
Expanded the list under “Tonality System” and clicked “Open Pythagorean”.
Under “Open Pythagorean”, clicked the third icon, “Edit Tonality System.”
In the “Edit Tonality System” window that opens,
under “Divisions”, for each interval, changed the “Divisions for specific intervals:” to numbers close to their Pythagorean values;
under “Accidentals”, for each accidental, clicked the third icon “Edit Accidental”, and in the window that opens, changed the “Pitch delta:” to numbers close to their Pythagorean values, then clicked “OK”;
under “Custom Key Signatures”, clicked the first icon “New Key Signature”, and for each key from 7b’s to 7#’s, created a new, custom key signature using the now-modified accidentals that appear under “Accidentals”, then clicked “OK”; then
clicked “OK”.
Again changed the tonality system of the piece to “Open Pythagorean”, following the procedure in the Dorico 6.0 / 6.1 manual “Changing the tonality system”, except that I did not do the last step, “4. Input a new key signature.”
For the last step,
under “Used in This Flow”, if I click on a clef icon, the tonality system reverts to the original 12-EDO;
under “Key Signatures”, if I click on the now blank (i.e., no sharps or flats), grayed-out clef icon, all accidentals disappear, and all pitches corresponding to the pre-blanked-out key signature become marked with natural accidentals; and
under “Custom Key Signatures”, if I click on a key signature, all accidentals disappear, and all pitches corresponding to the clicked-on key signature become marked with natural accidentals.
Comments:
All accidentals disappear whether the number of divisions of the octave is divisible by 12 or not.
All accidentals disappear regardless of the original, 12-EDO key signature, including “atonal”.
Dorico correctly recognizes the original 12-EDO system if saved under a different name, and does not alter anything in the score. That’s why I started with Dorico’s original 12-EDO system and made as few changes as possible, which were only to the numerical values of the tuning intervals between or associated with existing objects.
FWIW, if I open “Edit Tonality System” for the default “Equal temperament (12-EDO)”, under “Accidentals”, the natural is characterized by the ratio 0/665, and not 0/12. 665 happens to be a number of equal divisions of the octave I had been playing with in Dorico 5 and maybe Dorico 4. How did it get here? The denominator in the ratios for all the other accidentals is correctly 12.
I can’t find a userlibrary.xml file for Dorico 6, and the userlibrary.xml files I do find are for previous Dorico versions and do not contain the pitch and accidental division numbers I put into the Open Pythagorean tonality system for this example. Has the name of the file containing this information been changed?
Here are before & after pics:
